Review and Comparison of Computational Approaches for Joint Longitudinal and Time‐to‐Event Models

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/1/insr12322.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/2/insr12322_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/3/Supplement_ReviewComputationalJointModels_final.pd

Modelling recurrent events: a tutorial for analysis in epidemiology

In many biomedical studies, the event of interest can occur more than once in a participant. These events are termed recurrent events. However, the majority of analyses focus only on time to the first event, ignoring the subsequent events. Several statistical models have been proposed for analysing multiple events. In this paper we explore and illustrate several modelling techniques for analysis of recurrent time-to-event data, including conditional models for multivariate survival data (AG, PWP-TT and PWP-GT), marginal means/rates models, frailty and multi-state models. We also provide a tutorial for analysing such type of data, with three widely used statistical software programmes. Different approaches and software are illustrated using data from a bladder cancer project and from a study on lower respiratory tract infection in children in Brazil. Finally, we make recommendations for modelling strategy selection for analysis of recurrent event data

Joint models of longitudinal and time-to-event data with more than one event time outcome: a review

Methodological development and clinical application of joint models of longitudinal and time-to-event outcomes have grown substantially over the past two decades. However, much of this research has concentrated on a single longitudinal outcome and a single event time outcome. In clinical and public health research, patients who are followed up over time may often experience multiple, recurrent, or a succession of clinical events. Models that utilise such multivariate event time outcomes are quite valuable in clinical decision-making. We comprehensively review the literature for implementation of joint models involving more than a single event time per subject. We consider the distributional and modelling assumptions, including the association structure, estimation approaches, software implementations, and clinical applications. Research into this area is proving highly promising, but to-date remains in its infancy

Frailty multi-state models for the analysis of survival data from multicenter clinical trials

Proportional hazards models are among the most popular regression models in survival analysis. Multi-state models generalise them in the sense of jointly considering different types of events along with their interrelations, whereas frailty models introduce random effects to account for unobserved risk factors, possibly shared by groups of subjects. The integration of frailty and multi-state methodology is interesting to control for unobserved heterogeneity in presence of complex event history structures, particularly appealing in multicenter clinical trials applications. In the present thesis we propose the incorporation of nested frailties in the transition-specific hazard function; then, we develop and evaluate both parametric and semi-parametric inference. Simulation studies, performed thanks to an innovative method for generating dependent multi-state survival data, show that parametric inference is correct but extremely imprecise, whilst semiparametric methods are very competitive to evaluate the effect of covariates. Two case studies are presented, relative to cancer multicenter clinical trials. The multi-state nature of the models allows to study the treatment effect taking into account intermediate events, while the presence of frailties reduces the attenuation effect due to clustering. Finally, we present two new software tools, one to fit parametric frailty models with up to twenty possible combinations of baseline and frailty distributions, and one implementing semiparametric inference for multilevel frailty models, essential to fit the new nested frailty multi-state models

Methods for analysis of multi-state survival data

Tese de doutoramento em Ciências (área de especialização em Matemática)This thesis is concerned with multi-state survival analysis. In this context, we propose methods for the analysis of multi-state survival data. The methods developed in this thesis are motivated by the applications to the medical sciences. However, they can also be applied to economics, astronomy, and engineering, among other elds. This is an exciting and full potential area of research, with many interesting problems. Survival Analysis is concerned with studying inter-event times. In a classical setup, the focus is on the elapsed time between two well-de ned events: the starting event (\alive"), and the terminating event (\death"). Multi-state models can be considered as a generalization of the survival process where \death" is the ultimate outcome, but where intermediate states are identi ed. If the events are of the same nature, this is usually referred as recurrent events, whereas if they represent di erent states they are usually modelled through their intensity functions. When analyzing recurrent event data, the inter-event times are referred to as the gap times, and they are of course determined by the times at which the recurrences take place (i.e. the recurrence times). The statistical analysis of consecutive gap times is an issue of much importance. Most of the times, one will be interested in describing not only the marginal distribution of the gap times but also the bivariate distribution of the joint gap times. This will be considered in Chapter 2. Speci cally, we propose methods for estimate the bivariate distribution under right censoring and conditional bivariate distribution given a quantitative covariate. Alternatively, we may think the gap times as arising from a particular multi-state model such as the progressive three-state model or the progressive k-state model. A multi-state model is a model for a stochastic process, which is characterized by a set of states and the possible transitions among them. The states represent di erent stages of the disease course along a follow-up. Several multi-state models that have been widely used in biomedical applications but the three-state progressive model and the illness-death model are certainly the most common. The illness-death model is a generalization of the three-state progressive model in which a direct transition from the\alive"state to the nal, absorbing\dead"state is possible. In this model one of the major goals is the estimation of the so-called transition probabilities. Traditionally, this estimation is performed under a Markov assumption, which leads to the socalled Aalen-Johansen estimator. Unfortunately, the variance of this estimator may be large in heavily censored scenarios. The possibility of improving this estimator via presmoothing is explored in Chapter 3. For the practical application of the methods presented in Chapters 2 and 3, we developed several functions in R (R Development Core Team, 2013). Some of these functions were used to build an R package for the estimation of the bivariate distribution function. Details about this and other packages for multi-state modelling are given in Chapter 4. All methods are illustrated by means of its application to real biomedical datasets.Esta tese está focada na análise de sobrevivência multiestado. Neste contexto, propusemos métodos para a análise de dados de sobrevivência multiestado. Os métodos desenvolvidos nesta tese foram motivados pelas aplicações na medicina. No entanto, estes podem ser aplicados à economia, astronomia e engenharia entre outros campos. É uma área excitante e de grande potencial de investigação, com muitos problemas interessantes. A análise de sobrevivência preocupa-se com o estudo de tempos entre eventos. Numa versão clássica, o foco é sobre o tempo decorrido entre dois eventos bem definidos: o evento inicial ("vivo"), e o evento nal ("morte"). Os modelos multiestados podem ser considerados como uma generalização de um processo de sobrevivência onde "morte" é o resultado final, mas onde estados intermédios são identificados. Se os eventos são da mesma natureza, estamos no contexto de eventos recorrentes; se os estados representam diferentes eventos então eles são habitualmente modelados através de funções de intensidade. Na análise de dados de eventos recorrentes, os tempos entre eventos são usualmente referidos como "gap times", e são determinados pelos tempos onde as recorrências ocorrem (ou seja, tempos de recorrência). A análise estat ística de "gap times" consecutivos é um tema que tem recebido muita atenção nos últimos anos. Na maioria das vezes, não estão só interessados em descrever a distribuição marginal dos "gap times", mas também a distribuição bivariada conjunta dos mesmos. Isto será considerado no Capítulo 2. Especificamente, propusemos métodos para estimar a distribuição bivariada na presença de censura e a distribuição bivariada condicional, dada uma covariável quantitativa. Alternativamente, pensamos nos "gap times" como resultado de um modelo multiestado particular tal como modelo progressivo de três estados ou modelo progressivo de k-estados. Um modelo multiestado é um modelo para um processo estocástico, que é caracterizado por um conjunto de estados e possíveis transições entre eles. Os estados representam diferentes etapas do percurso da doença ao longo de um acompanhamento "follow up". Vários modelos multiestados têm sido amplamente utilizados em aplicações biomédicas, mas o modelo progressivo de três estados e o modelo doença-morte são os mais comuns. O modelo doença-morte e a generalização do modelo progressivo de três estados em que uma transição direta do estado "vivo" para o final, estado absorvente "morte" é possível. Neste modelo um dos principais objetivos é a estimativa das probabilidades de transição. Tradicionalmente, esta estimativa é calculada sob o pressuposto de Markov, que tradicionalmente recorre ao estimador de Aalen-Johansen. Infelizmente, a variância deste estimador pode ser elevada em cenários com elevadas taxas de censura. A possibilidade de melhorar este estimador com pré-suavização é explorada no Capí tulo 3. Para aplicações práticas dos métodos presentes no Capítulo 2 e 3, desenvolvemos várias funções em R (R Development Core Team, 2013). Algumas dessas funções foram usadas para construir um package no R para estimar a função distribuição bivariada. Detalhes sobre este package e outros packages para modelação multiestado são dados no Capítulo 4. Todos os m étodos serão ilustrados por meio da sua aplicação em dados reais em medicina.Portuguese Ministry of Science, Technology and Higher Education in the form of grant SFRH/BD/62284/2009 and by Programa Operacional Factores de Competitividade COMPETE and by research Centre of Mathematics of the University of Minho through FCT - Funda c~ao para a Ci^encia e a Tecnologia, within the Project Est-C/MAT/UI0013/2011 and CMAT

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)

Bayesian Models for Joint Longitudinal and Multi-State Survival Data

Biomedical data commonly include repeated measures of biomarkers and disease states over time. When the processes determining the biomarker levels and disease states are related, a joint longitudinal and survival model is needed to properly handle the data. In a recent study of adrenal cancer patients at the University of Michigan, their tumors were monitored with repeated radiography scans. Other body measurements, called morphomics, were also measured from these scans. At each scan, it was noted whether the patient's disease was stable, progressing or regressing. In addition, the data include time to death or end of follow-up. Motivated by this data we explore joint models for longitudinal and survival data of several types. In Chapter 2 we compare computational approaches to joint longitudinal and survival models with a single type of event. We examine different joint model formulations especially those most often implemented in software available to statisticians and clinicians. We apply and compare several models to the adrenal data and perform a simulation study to further evaluate each model and software. In Chapter 3 we examine the relationship between a morphomic variable and time to first disease state change which can be either cancer progression or regression, in the adrenal cancer data. We develop Bayesian joint models for longitudinal and competing risks survival data. A seldom considered aspect of competing risk joint models is the relationship between the two competing outcomes. This cannot be examined when using the most common technique, cause-specific hazards models. With that motivation for our future projects, we work under the assumption that each risk has a latent failure time for each individual. We begin with the simple case of conditionally independent risks and model the survival times using parametric distributions. We apply our models to the adrenal data and examine the performance via simulations. In Chapter 4 we extend our joint longitudinal and competing risks models for dependent competing risks. We begin with a discussion of survival copulas and the general joint survival function we will use which is based on an Archimedean copula model. We prove that dependent variables with this joint survival function can be written in terms of independent variables which is useful for simulating data. We develop the model with Weibull marginals. We fit this model to the adrenal data and examine the models using a simulation study. We discuss interpretations of the model and how it can be used to learn about the dependence between risks. Finally, in Chapter 5 we will develop a joint model that incorporates multiple longitudinal outcomes and multistate survival data. We will develop an appropriate model and apply it to the adrenal cancer data.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169659/1/acullen_1.pd

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio